Singularity of non‐pluripolar cohomology classes

Abstract

We establish a relation between Lelong numbers and the full mass property of relative non‐pluripolar products. We use this relation to prove that if the restricted volume of a big class along an effective divisor has full mass, then the Lelong numbers of the non‐pluripolar class at every point in the support of are zero. In particular, we obtain that on projective manifolds, the Lelong numbers of the non‐pluripolar class of a big class are zero.